# Dynamic properties of asymmetric double Josephson junction stack with quasiparticle imbalance

## TL;DR

This paper investigates how quasiparticle charge imbalance affects the dynamics of an asymmetric double Josephson junction stack, revealing complex switching behaviors and hysteresis effects in current-voltage characteristics.

## Contribution

It provides analytical and numerical analysis of quasiparticle imbalance effects on asymmetric Josephson stacks, highlighting new switching phenomena and hysteresis in I-V characteristics.

## Key findings

- Switching of the fast junction increases the effective critical current of the slow junction.
- Initial switching of the slow junction can either increase or decrease the fast junction's critical current.
- Slow quasiparticle relaxation causes additional hysteresis in the current-voltage characteristics.

## Abstract

We study analytically and numerically the influence of the quasiparticle charge imbalance on the dynamics of the asymmetric Josephson stack formed by two inequivalent junctions: the fast capacitive junction $JJ_{1}$ and slow non-capacitive junction $JJ_{2}$. We find, that the switching of the fast junction into resistive state leads to significant increase of the effective critical current of the slow junction. At the same time, the initial switching of the slow junction may either increase or decrease the effective critical current of the fast junction, depending on ratio of their resistances and the value of the capacitance. Finally, we have found that the slow quasiparticle relaxation (in comparison with Josephson times) leads to appearance of the additional hysteresis on current-voltage characteristics.